Question

physics - fall 2025
thermo calculations 2
q = mcδt
q = mh
c_{water}=4.18j/g°c
h_v = 2260j/g
h_f = 334j/g
vaporize water
freeze water

1. how much heat does it take your water heater to raise the temperature of 50 l of water by 40°c (1 l = 1000 g)?
2. how much heat does it take to melt 5 kg (1 kg = 1000 g) of ice to make water?
3. how much heat does it take to boil 2 l of water (1 l = 1000 g)?
4. how much water could you boil by burning a 16 gallon car tank of gasoline? (1 gallon gasoline = 131,000,000 j)
5. what is the specific heat of a metal that requires 4500 j to heat 50 g of the metal by 160°c?
6. if you want to warm up a 250 g iron hammer by 50°c how much energy will it take? (c = 0.45 j/gc)

Explanation:

Question 1

Step1: Convert volume to mass

Given \(1L = 1000g\), for \(V = 50L\) of water, \(m=50\times1000 = 50000g\)

Step2: Use heat formula \(Q=mc\Delta T\)

\(c = 4.18J/g^{\circ}C\) (specific heat of water), \(\Delta T=40^{\circ}C\)
\(Q=(50000g)\times(4.18J/g^{\circ}C)\times40^{\circ}C\)
\(Q = 50000\times4.18\times40\)
\(Q=8360000J\)

Step1: Use latent - heat formula \(Q = mH_f\)

Given \(m = 5kg=5\times1000g = 5000g\), \(H_f = 334J/g\) (latent heat of fusion of ice)
\(Q=(5000g)\times(334J/g)\)

Step1: Convert volume to mass

For \(V = 2L\) of water, \(m = 2\times1000g=2000g\)

Step2: Use latent - heat formula \(Q = mH_v\)

\(H_v=2260J/g\) (latent heat of vaporization of water)
\(Q=(2000g)\times(2260J/g)\)

Answer:

\(8360000J\)

Question 2